Handbook 1996 : Faculty of Science (Volume 4 page 211)
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618-252 "Analysis" appears differently in several places - choose the one you want:

1. 618-252 Mathematics, Faculty of Science.
2. 618-252 Math. & Stats., Faculty of Educ(Parkville).

1. Mathematics, Faculty of Science (v4, p211) : Next:618-261 | Prev:618-251

618-252 Analysis

Credit points: 12.0

Coordinator: Dr M Ross

Prerequisite: Mathematics 618-102 (1995 Handbook) or any of 618-112, 618-122, 618-200, 618-211.

Contact: 39 lectures (three a week).

Timetable: Second semester

Objectives:

On completion of this subject, students should:

Comprehend:

• the concept of convergence of sequences and series; elementary topology of the real line;
• the fundamentals of continuity, differentiability of functions of several real variables;
• the concepts of an analytic function of a complex variable; complex derivative; power and Laurent series in complex variables;
• basic topological concepts in the complex plane;
• Cauchy's theorem and its applications;

Have developed:

• skills in determining the convergence or otherwise of sequences and series;
• skills in differentiating functions of a complex variable;
• skills in calculating contour integrals;
• the ability to work with analytic functions in the cut plane;
• the ability to apply Cauchy's integral formula and the residue theorem;

Appreciate:

• differences between functions of a real and a complex variable;
• the role of complex analytic methods in solving important problems in science and engineering.

Content:

Sequences and Series: standard sequences and series, Cauchy convergence, ratio and n-th root tests, absolute and conditional convergence, re-arrangements, power series. Continuity: continuity and differentiability of functions of several real variables. Functions of a complex variable: elementary functions of a complex variable, branches; differentiation, analytic functions, Cauchy-Riemann equations. Integration:line and contour integrals, Cauchy's integral theorem; Laurent series; singularities, poles, Liouville's theorem; residue theorem, limiting contours, evaluation of integrals using contour integration.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

Note. Credit cannot be gained for both 618-202 and 618-252.

1. Mathematics, Faculty of Science (v4, p211) : Next:618-261 | Prev:618-251

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-261 | Prev:618-251

618-252 Analysis

Note: Credit cannot be gained for both 618-202 and 618-252.

Credit points: 12.0

Coordinator: Dr M Ross.

Prerequisite: Mathematics 618-102 (1995 Handbook) or any of 618-112, 618-122, 618-200, 618-211.

Contact: 39 lectures (three each week)

Timetable: Second semester.

Objectives:

On completion of this subject, students should:

Comprehend:

• the concept of convergence of sequences and series; elementary topology of the real line;
• the fundamentals of continuity, differentiability of functions of several real variables;
• the concepts of an analytic function of a complex variable; complex derivative; power and Laurent series in complex variables;
• basic topological concepts in the complex plane;
• Cauchy's theorem and its applications;
• Have developed:
• skills in determining the convergence or otherwise of sequences and series;
• skills in differentiating functions of a complex variable;
• skills in calculating contour integrals;
• the ability to work with analytic functions in the cut plane;
• the ability to apply Cauchy's integral formula and the residue theorem;

Appreciate:

• differences between functions of a real and a complex variable;
• the role of complex analytic methods in solving important problems in science and engineering.

Content:

Sequences and Series Standard sequences and series, Cauchy convergence, ratio and n-th root tests, absolute and conditional convergence, re-arrangements, power series. Continuity Continuity and differentiability of functions of several real variables. Functions of a complex variable Elementary functions of a complex variable, branches; differentiation, analytic functions, Cauchy-Riemann equations. Integration Line and contour integrals, Cauchy's integral theorem; Laurent series; singularities, poles, Liouville's theorem; residue theorem, limiting contours, evaluation of integrals using contour integration.

Assessment:

Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.

* Note that ASSESSMENT, CONTACT, CONTENT, NOTE, OBJECTIVES differs from the maintainer's version above. A log of variations is available.

2. Math. & Stats., Faculty of Educ(Parkville) (v5, p147) : Next:618-261 | Prev:618-251

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Status:          Official 1996
Date created:    Oct  9 1995
Last modified:   Oct  9 1995
Authorised by:   Academic Registrar
Email enquiries: Course_Information@registrar.unimelb.edu.au

Copyright © University of Melbourne 1995,1996.